- A particle \(P\) of mass 2 kg moves in a straight line along a smooth horizontal plane. The only horizontal force acting on \(P\) is a resistance of magnitude \(4 v \mathrm {~N}\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is its speed. At time \(t = 0 \mathrm {~s} , P\) has a speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find \(v\) in terms of \(t\).
(6)
\begin{figure}[h]
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\caption{Figure 1}
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\end{figure}
A girl swims in still water at \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). She swims across a river which is 336 m wide and is flowing at \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). She sets off from a point \(A\) on one bank and lands at a point \(B\), which is directly opposite \(A\), on the other bank as shown in Fig. 1. Find
- the direction, relative to the earth, in which she swims,
- the time that she takes to cross the river.